Chapter 3, Problem 3.15CYS

To determine

To find: The variable that is most likely to have a normal distribution.

Answer to Problem 3.15CYS

The correct option is (c) Lengths of 100 newborns in Connecticut.

Explanation of Solution

Reason for correct answer:

The variables are most likely to have a normal distribution if the scores on tests taken by many people have repeated measurements of the same quantity and the characteristics of biological populations.

Here, the lengths of 100 newborns in Connecticut are taken by the characteristics of biological populations. That is, the lengths of newborns are in a particular range of values and there are few babies with very less or more lengths that indicate a bell shape curve. Thus, the variables of the lengths of 100 newborns in Connecticut are most likely to have a normal distribution.

Hence, the correct option is (c) Lengths of 100 newborns in Connecticut.

Reason for incorrect answers:

As the age of the person increases, the income decreases. The variable of income per person for 150 different countries is skewed to the right.

Also, the variable sale price of 200 homes in Santa Barbara, California is skewed to the right because there would be few homes with higher prices.

Hence, options (a) and (b) are not correct.

Conclusion:

Thus, the variables of the lengths of 100 newborns in Connecticut are most likely to have a normal distribution.

Statistics Concept Introduction

Introduction:

Normal distribution:

For any continuous random variable x whose graph of distribution is symmetric, peaked and bell shaped is known as normal distribution.